What is the role of benzoyl peroxide in addition polymerization of alkenes? Explain its mode of action with the help of an example.

(N/A) Benzoyl peroxide acts as a free radical initiator in the addition polymerization of alkenes. It undergoes homolytic fission to produce free radicals,which then initiate the polymerization process. The mechanism involves three steps:
$(i)$ Chain initiation step:
$C_6H_5-CO-O-O-CO-C_6H_5$ $\rightarrow 2C_6H_5-CO-O$ $\rightarrow 2C_6H_5^{\bullet} \text{ (Phenyl radical)}$
$(ii)$ Chain propagation step:
$C_6H_5^{\bullet} + CH_2=CH_2$ $\rightarrow C_6H_5-CH_2-CH_2^{\bullet}$ $\rightarrow C_6H_5-(CH_2-CH_2)_n-CH_2-CH_2^{\bullet}$
$(iii)$ Chain termination step:
$2C_6H_5-(CH_2-CH_2)_n-CH_2^{\bullet}$ $\rightarrow C_6H_5-(CH_2-CH_2)_n-CH_2-CH_2-CH_2-CH_2-(CH_2-CH_2)_n-C_6H_5 \text{ (Polythene)}$